Problem: Ashley is 4 times as old as Omar. Six years ago, Ashley was 7 times as old as Omar. How old is Omar now?
Answer: We can use the given information to write down two equations that describe the ages of Ashley and Omar. Let Ashley's current age be $a$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $a = 4o$ Six years ago, Ashley was $a - 6$ years old, and Omar was $o - 6$ years old. The information in the second sentence can be expressed in the following equation: $a - 6 = 7(o - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to use our first equation for $a$ and substitute it into our second equation. Our first equation is: $a = 4o$ . Substituting this into our second equation, we get: $4o$ $-$ $6 = 7(o - 6)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $4 o - 6 = 7 o - 42$ Solving for $o$ , we get: $3 o = 36.$ $o = 12$.